Intensification of Large-Scale Stretching of Atmospheric Pollutant

DECEMBER 2017 H A S Z P R A 4229

Intensiﬁcation of Large-Scale Stretching of Atmospheric Pollutant Clouds due to Climate Change

TÍMEA HASZPRA Institute for Theoretical Physics, and MTA-ELTE Theoretical Physics Research Group, Eotv€ os€ Loránd University, Budapest, Hungary

(Manuscript received 25 April 2017, in ﬁnal form 28 September 2017)

ABSTRACT

The aim of the paper is to investigate the question of how a changing climate inﬂuences the spreading of pollutants on continental and global scales. For characterizing the spreading, a measure of chaotic systems, called topological entropy, is used. This quantity describes the exponential stretching of pollutant clouds and, therefore, is related to the predictability and the complexity of the structure of a pollutant cloud. For the dispersion simulations the ERA-Interim database is used from 1979 to 2015. The simulations demonstrate that during this period the mean topological entropy slightly increases: the length of an initially line-like pollutant cloud advected for 10 (30) days in the atmosphere becomes 20%–65% (200%–400%) longer by the 2010s than in the 1980s. The mean topological entropy is found to be strongly correlated with the mean of the absolute value of the relative vorticity and only weakly linked to the mean temperature.

1. Introduction in which pollutants rise high intheatmosphereandmayhave continental and global impacts are particularly important. One of the most challenging problems of the present Although there are studies dealing with the connection day is the assessment of the consequences of climate between climate change and air quality (e.g., Bytnerowicz change, several of which are not yet explored satisfac- et al. 2007; Kinney 2008), these mainly focus on regional torily. To the best of our knowledge, one aspect that has or local scales or the changes in pollutant concentration, not been investigated yet is the impact of climate change rather than the transport itself (Ma et al. 2004; Jacob and on the large-scale atmospheric transport processes— Winner 2009; Fang et al. 2011). Thus, the purpose of this that is, the investigation of the change in the characteristics of the spreading (e.g., speed and predictability, research is to ﬁll the gap and carry out a detailed analysis or the structure) of pollutant clouds. to reveal whether the intensity of the large-scale transport Recently, two major events drew attention to the po- processes is altered or not by the changing climate. In tentially important consequences of large-scale atmo- this paper, we focus on the past decades and investigate spheric transport: the ash plumes of the Eyjafjallajökull the instrumentally observed climate change (IPCC 2013) volcano’s eruption in 2010, which resulted in airspace for the time period from 1979 to present. With the help of closures over Europe (e.g., Flentje et al. 2010), and the dispersion simulations based on atmospheric reanalysis radioactive material released during the accident of the data we are able to investigate a large number of events Fukushima Daiichi nuclear power plant, which caused distributed uniformly in time and space, so that they are measurable effects far away from the source, even in suitable for a statistical analysis to investigate whether the the United States and Europe (e.g., Lujaniene_ et al. characteristics of atmospheric spreading are altered or 2012; MacMullin et al. 2012; Mészáros et al. 2016). not on a detectable level in the past 37 yr. Therefore, the investigation and modeling of the events In the case of large-scale atmospheric dispersion, in which the characteristic time scale is on the order of 10 days, the typical horizontal distance of the transport Denotes content that is immediately available upon publica- of pollutants by the mean wind is on the order of tion as open access. 1000 km. Meanwhile, for the horizontal turbulent diffusion the characteristic length scale is about 3–30 km Corresponding author:Tímea Haszpra, [email protected] (Haszpra and Tél 2013b). Therefore, as a ﬁrst approximation,

DOI: 10.1175/JAS-D-17-0133.1 Ó 2017 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses). Unauthenticated | Downloaded 09/26/21 02:18 PM UTC 4230 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74

FIG. 1. (left) Advection image of a 38-long line segment (n0 5 1000 particles, initiated at 0000 UTC 1 Dec 2015 at 408N, 908E at 500 hPa) on the tenth day after the emission. Color bar indicates the pressure coordinate (hPa) of the particles. The initial position of the line segment is marked by the green line surrounded by the black square. (right) The length of the filament in time [solid line, determined as in Eq. (4)] and the fitted exponential function (dashed 2 line) with exponent h 5 0.81 day 1. the stochastic part of the dispersion, that is, the effect of pollutants (Haszpra and Tél 2013b). A pollutant cloud turbulent diffusion, can be neglected in the calculation typically spreads in the atmosphere in a folded, fila- of the transport of the pollutants. In this study, we consider mentary structure as illustrated by Fig. 1. The figure the pollutant to be an inert gas. Because most of the time shows the advection pattern of a pollutant cloud that the pollutants are transported in the free atmosphere, de- consists of a large number of tracer particles, which position processes do not have a significant role. Hence, the form a 38-long line segment on the 500-hPa level at the transport of the pollutant is determined only by the advec- beginning of the simulation (see the green line within tion process, which is deterministic. In the particle-tracking the black square). One can see that within 10 days the method applied in this study, the motion of a particle is de- filament becomes highly stretched and folded as a result scribed by three time-dependent, deterministic ordinary of the shearing and mixing effects of the atmospheric differential equations. In a dynamical system described by flow and covers a large part of the hemisphere. It is such a set of equations, chaotic behavior can occur; that is, worth noting that the effects of two cyclones are no- the dynamics can be sensitive to the initial conditions, making ticeable in the lower-left part of the left panel. These it unpredictable for an extended time (Ottino 1989; Ott 2002). cyclones force the pollutant particles to converge toward To analyze the impact of a changing climate on the their centers by forming spirals and lift the particles high large-scale transport processes, we use a measure of (marked by dark blue) in the atmosphere. chaos called the topological entropy (Newhouse and If the pollutant clouds are initialized as line segments, Pignataro 1993; Ott 2002; Tél and Gruiz 2006). In the the length L of the filaments typically increases expo- context of large-scale transport, topological entropy nentially over time t: describes the stretching rate of the pollutant clouds. As a measure of folding, it also describes the complexity L ; exp(ht), (1) of the structure of the pollutant cloud and the intensity and predictability of the spreading of the pollutant. As where the exponent h denotes the topological entropy, a rule of thumb, a larger value of the topological entropy that is, the stretching rate. This process is illustrated by implies the coverage of a larger geographical area by the right panel of Fig. 1, in which the fitted exponential

Unauthenticated | Downloaded 09/26/21 02:18 PM UTC DECEMBER 2017 H A S Z P R A 4231 function from day 2 to day 10 is marked by the dashed raindrops and aerosol particles. RePLaT was tested by line. The length of the filament increases by a factor of simulating the dispersion of volcanic ash from volcanic about 3000 during the investigated time period. Note eruptions such as the ones of Eyjafjallajökull and Mount that a line segment cannot split up into two or more Merapi (Haszpra and Tél2011, 2013a) and by simulating branches, because it would require a wind vector that the dispersion and deposition of the radioactive particles points in more than one direction at some location. As a released during the accident of the Fukushima Daiichi consequence, a line segment remains a line segment nuclear power plant (Haszpra and Tél2016). In the for- forever, and the determination of the full (folded) length mer studies reasonable agreement was found between the is unambiguous. For more details on the topological distribution of volcanic ash in the simulation and that entropy, see, for example, Thiffeault (2010); Budisic´ and indicated by satellite measurements. In the case of the Thiffeault (2015), and Haszpra and Tél (2013b) in the Fukushima Daiichi accident the arrival times of the pol- atmospheric context. lution at different locations coincided with the observa- At the mid- and high latitudes, the characteristic values tion, and the simulations were able to reproduce the 2 of h are found to be 0.6–0.8 day 1, which indicates a measured concentrations of the noble gas 133Xe with ac- stretching of the filaments by a factor of 400–3000 within ceptable accuracy. 10 days. The stretching rate of pollutant clouds is de- In this paper, the calculation of the particle trajecto- pendent on the season (Haszpra and Tél2013b). There- ries are carried out with the simplest configuration, in fore, it is plausible to assume that it also depends on the which only advection is considered. In the simulations, changing state of the climate. As the stretching rate is the ideal tracers, corresponding to inert gases or infinitesi- exponent that describes the exponential growth, small mally small air parcels, are tracked. In this case, the deviations in its value result in significant differences in velocity vp of a particle equals to the velocity v of the the length of the expanding clouds. For example, the wind at the location rp of the particle at time t, and 2 2 2 slight increase of 10 3 day 1 yr 1 in the stretching rate the equation of motion of the particles is over 37 yr would result in a change of about 50% and 300% increase of the length after 10 days and a month, _ [ 5 rp(t) vp(t) v[rp(t), t]. (2) respectively. The paper is organized as follows. Section 2 provides a In the present study, if a tracer particle encounters brief overview of the Real Particle Lagrangian Trajec- with the surface, it bounces back to the atmosphere tory (RePLaT) model (Haszpra and Tél 2013a; Haszpra by a perfectly elastic collision. RePLaT determines and Horányi 2014) and the equations of motion by which the particle trajectories in longitude–latitude–pressure the trajectories of the pollutant particles that form the coordinate system using Euler’s method, that is, the pollutant clouds are determined. It also includes the position rp of a particle at time t 1Dt is calculated as description of the meteorological data and the initial setup of the simulations. The results are presented in 1D 5 1 D rp(t t) rp(t) v[rp(t), t] t. (3) section 3, and section 4 summarizes the main conclu- sions of the work. The meteorological data required for the trajectory calculation, that is, the wind field with zonal u, meridional y,andverticalv velocity components in pressure co- 2. Equations, data, and methods ordinates [v 5 (u, y, v)], as well as variables necessary for For the simulation of the spreading of the atmospheric analyzing the climatic impact [e.g., the temperature fields pollutant clouds the RePLaT atmospheric dispersion T,geopotentialfieldsF, and potential vorticity fields model is used. RePLaT is a Lagrangian trajectory model (PV)], are ERA-Interim data from the European Centre that tracks individual spherical particles with fixed, re- for Medium-Range Weather Forecasts (ECMWF) (Dee alistic radius and density. The velocity is given by the et al. 2011) on a 1.5831.58 horizontal grid with 6-h time Newtonian equation of motion of a finite-size particle in a resolution. The time step we use in RePLaT in this study prescribed wind field, and in the vertical direction de- is the same Dt 5 45 min as in Haszpra and Tél(2013b),as position is also taken into account. RePLaT can reckon it proved to be sufficiently small for free-atmospheric with the effect of turbulent diffusion on the particles transport simulations. as a stochastic term in the equations of motion, and it For the computation of the topological entropy can simulate the scavenging of particles by precipitation (stretching rate) we take line segments of initial length as a random process that results in a particle being cap- of 38’330 km at p0 5 500 hPa in the free atmosphere tured by a raindrop with a probability depending on that consist of n 5 103 uniformly distributed ideal par- the precipitation intensity and the collision efficiency of ticles and we track these degenerate ‘‘pollutant clouds’’

Unauthenticated | Downloaded 09/26/21 02:18 PM UTC 4232 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74 for 10 days. When the distance of two neighboring particles exceeds 10 km, a new particle is inserted between them. Owing to the exponential stretching of a line segment, the number of particles in the simulations increases (not uniformly along the ﬁlament) and can reach n 5 106 after 10 days, while its average is on the order of 104. To gain a global picture, 12 3 17 meridional line segments are located on a geographical grid over the globe from l0 5 1508W to 1808 in increments of 308 and from u0 5 808Sto808N in increments of 108. The length of a ﬁlament at time t is calculated by the sum of the distances between its particles:

n21 5 å j 2 j L(t) rp,i(t) rp,i11(t) , (4) i51 where rp,i is the position of the ith particle. Since vertical 2 2 stretching proved to be 10 2–10 3 times smaller than the horizontal one in our previous study (Haszpra and Tél 2013b), we also neglect it in this paper. Thus, the length of a ﬁlament is obtained from the horizontal distances between particle pairs, and the distance (km) is calculated along great circles by j 2 j 5 u u rp,i(t) rp,i11(t) arccos[sin p,i sin p,i11 1 u u l 2 l cos p,i cos p,i11 cos( p,i p,i11)]

3 180 3 : p 111 1, (5) where lp,i and up,i are the longitudinal and latitudinal co- p 3 FIG. 2. The zonal and seasonal means of the stretching rate h in ordinate of the ith particle, respectively, and (180/ ) (top) JJA and (bottom) DJF from 1979 to 2015. Each line connects 111.1 converts the unit from radians to kilometers using the the mean of the different latitudes for a given year. Lines are fact that the spherical distance of 18 along a great circle colored from blue to red from 1979 to 2015. corresponds to a length of 111.1 km along the surface. The filaments are tracked for a 10-day-long time period, characteristic to continental and global transport processes. It is and June–August (JJA) seasons. The line segments in- worth noting that tracking the particles for a much longer troduced in section 2 are generated every 10 days time could result in smaller geographical differences in the and tracked for 10-day periods. The length of the line topological entropy, because line segments of the mid- and segments is computed at each time instant and an high latitudes are mixing in the hemisphere rapidly and exponential function is fitted to the resulting data may cover almost a whole hemisphere within about a from day 2 to day 10 to obtain an estimate of the value month (Haszpra and Tél 2013b). of the stretching rate h. Figure 2 illustrates the zonal- and seasonal-mean 3. Results values of the stretching rate from 1979 to 2015 during JJA and DJF. The curves for the later years, which a. Time evolution of the stretching rate due to climate are marked by warmer colors, have generally some- change what higher values at each latitude. The values for the 2 To find a relationship between changing climate different years range from 0.05 to 0.15 day 1 over the conditions and the characteristics of the spreading, and globe. The distribution of the zonal-mean stretching to study the possible seasonal effects, we run dispersion rate, that is, the shape of the curves, does not change simulations with the RePLaT model for each year significantly over the 37 yr. One can also notice that in from 1979 to 2015 for the December–February (DJF) each year larger values characterize the mid- and high

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21 21 21 TABLE 1. The slopes of the curves in Fig. 3 (10 day yr ) with 95% conﬁdence intervals.

SM TR NM JJA 1.199 6 0.303 1.214 6 0.326 0.818 6 0.367 DJF 1.285 6 0.343 1.376 6 0.330 0.546 6 0.356

To provide further support to our initial conclusion about the increasing stretching rate values for the time period 1979–2015, Fig. 3 presents the time evolution of the areal mean of the stretching rate for 1979–2015

for different geographical regions: tropics (TR; u0 5 208S–208N), NH extratropics (NM; u0 5 308–808N), and SH extratropics (SM; u0 5 308–808S). Dashed lines indicate linear fits to the data, and their slopes are given in Table 1. The figure and the table show a slow, but definite, increase of the mean values of the stretching rates from 1979 to 2015, with fluctuations that are an order of magnitude smaller. The largest change is in the tropics, while the smallest one is in the NH extratropics. For example, the increase of the stretching rate from about 2 0.42 to 0.47 day 1 in the tropics in DJF implies an increase of the length of the 10-day-old filaments by a 2 2 factor of about exp(0:47 day 1310 day)/exp(0:42 day 13 10 day) 5 exp(0:5) ’ 1:65. The same factor for the NH extratropics in DJF, where the stretching rate increases 2 from about 0.62 to 0.64 day 1, is 1.22. A formal extrapolation of the results for a 30-day period would suggest that the length of the filaments advected in the atmosphere for a month can be 4.5 times larger in the 2010s FIG. 3. The regional and seasonal means of the stretching rate h than in the 1980s in the tropics and SH extratropics and with the standard deviation of the seasonal-mean values for TR, 1.82 times larger in the NH extratropics. Obviously, fila- NM, and SM in (top) JJA and (bottom) DJF from 1979 to 2015. ments that originate in the tropics usually mix into the Dashed lines denote linear fits to the data with slopes in Table 1. midlatitudinal atmospheric circulation within 30 days, and vice versa, the filaments that originate in the extra- 2 latitudes (0.5–0.8 day 1), where more intense cyclonic tropics can mix into the tropics. Therefore the true mean activity takes place than in the tropical belt (0.3– stretching rates and length factors lie between the values 2 0.5 day 1), in all years. To demonstrate the large dif- obtained by extrapolation, assuming a complete separa- ference between the stretching rates of the different tion of the regions. regions, it is useful to consider a characteristic value of It is worth noting that while the order of magnitude 2 2 21 21 0.7 day 1 for the extratropics and 0.4 day 1 for the of the mean values is 10 day , the increase of the 24 23 21 21 tropics: they result in a length increase of a factor of 1100 stretching rate is on the order of 10 –10 day yr , and 55 over 10 days, respectively; that is, an almost twice- which represents a yearly increment on the order of as-large stretching rate is associated with an ;20-times- magnitude 2–3 times smaller than the mean values. longer filament. Both hemispheres have the maximum These values underline the fact that even the apparently values in their respective winter season, in which the cir- small increase in the stretching rate during the past culation is more active than in the summer season. The four decades leads to 20%–65% (200%–400%) longer average difference between the winter and summer sea- pollutant filaments after a 10 (30)-day advection. The sons is greater for the Southern Hemisphere (SH) than for importance of this result lies in the fact that it suggests the Northern Hemisphere (NH), which might be the that radioactive pollutants or pollutants from volcanic consequence of the larger portion of oceanic regions, eruptions could reach a significantly larger region in the which reduces the impact of lands on the wind. 2010s than in the 1980s.

Unauthenticated | Downloaded 09/26/21 02:18 PM UTC 4234 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 74 b. Relation to meteorological quantities Our next step is to find a relationship between the time evolution of the stretching rate and different meteorological variables. Finding a connection between the Lagrangian characteristics of the spreading of pollutants and the Eulerian features of climate would be useful in situations where the properties of the spreading would have to be estimated for a different climate, as it would not require a large number of computationally costly extra dispersion simulations. Because the stretching rate is calculated from particle positions, it is a Lagrangian quantity. Thus, one cannot expect to find an exact link between its behavior and the Eulerian meteorological fields unless the meteorological data are considered along the particle trajectories of the filaments. In the hope that an estimate of the change of the stretching rate can be obtained by utilizing only Eulerian information about the meteorological fields, without making transport simulations, we compare areal averages of the Eulerian meteorological fields for fixed regions (atmospheric volumes) with Eulerian fields of the mean stretching rate of pollutant clouds in the SM, TR, and NM region, rather than averaging over the grid cells covered by the particles, since the latter would only characterize a particular pollutant cloud, while the former is of regional relevance. As Fig. 1 illustrates, a filament that is initialized as a few-hundred-kilometer- long line segment often covers a significant region of a hemisphere after 10 days, and it rarely mixes into the other hemisphere within that time. Therefore, we select the latitudinal boundaries of the ‘‘boxes’’ (atmospheric volumes) for the predictions of the mean stretching rate of SM, TR, and NM to be 908S–08,458S–458N, and 08–908N, respectively. Motivated by the vertical extent of the evolved line segment in Fig. 1, the boundaries of the pressure levels have been chosen as 1000 and 100 hPa. In addition, the effect of considering single levels (300, 500, and 850 hPa and 315 and 330 K) has been also analyzed. Based on Eqs. (2) and (4), the stretching rate is fully determined by the wind field, and the stretching of a line segment can be linked to the spatial inhomogeneity of the velocity values along the filament (i.e., derivatives FIG. 4. The time evolution of the mean stretching rate hs and the jjj of the wind speed). Therefore, as a first step, we in- mean of the absolute value of the relative vorticity s, both stan- vestigate the relationship with the relative vorticity and dardized over time, for different pressure levels in JJA for (top) TR, (middle) NM, and (bottom) SM. shear stress. As climate change is mostly interpreted in terms of temperature change, the potential connection between the stretching rate and temperature, as well as often used for the identification of synoptic-scale the equator-to-pole temperature difference, is also an- weather systems, and horizontal wind speed and ki- alyzed at different atmospheric levels. Besides these, we netic energy, to provide a more comprehensive view also investigate other meteorological variables, such as of variables possibly influencing the evolution of the potential vorticity and geopotential heights, which are stretching rate.

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FIG. 5. The correlation coefﬁcient R of the mean stretching rate with (left) the mean of the absolute value of the relative vorticity for different pressure levels and (right) the mean of the absolute value of the potential vorticity anomaly for different isentropic levels with 95% conﬁdence intervals in (top) JJA and (bottom) DJF for TR, NM, and SM.

As an illustration, Fig. 4 presents the time evolution of pollutant line segments and the absolute value of the the mean stretching rate and the mean of the absolute relative vorticity/shear stress. value of the relative vorticity, both standardized over Based on the results of relative vorticity, it seems to be time for illustrative purposes, at the chosen pressure useful to investigate the relationship of the stretching levels for SM, TR, and NM in JJA. (Standardized quan- rate with potential vorticity, which is often applied in the tities for the time series of a general scalar state variable q investigation of the dynamics of cyclones (e.g., Davis are calculated as qs 5 (q 2 q)/sq,whereq is the temporal and Emanuel 1991; Stoelinga 1996; Möller and mean value of q and sq is the standard deviation of q over Montgomery 2000). Ertel potential vorticity is given by the investigated time interval.) The two quantities are PV 52g(ju 1 f )›u/›p, where g is the gravitational ac- apparently not independent of each other: usually the celeration, ju is the relative isentropic vorticity, f is the increase (decrease) in relative vorticity is associated with Coriolis parameter, u is the potential temperature, and p the increase (decrease) in stretching rate. To be more is the pressure. That is, PV is the product of the absolute quantitative, the left panels of Fig. 5 show the correlation vorticity and the static stability, therefore, consists of a coefficients for the time series of the two quantities. In all dynamical factor and a thermodynamic factor. While of the three regions the correlations are statistically sig- positive potential anomaly implies large cyclonic abso- nificant at the 95% level. The strongest correlations ex- lute vorticity and/or stronger stability, negative anomaly ceed 0.8 and are related to averages taken through the is associated with large anticyclonic absolute vorticity entire depth of the 1000–100 hPa layer of the atmosphere. and/or weaker static stability. In this paper the reference Note that considering only the data at the 300-, 500-, or state for the calculation of anomalies is chosen as in 5 2›u › 850-hPa level gives a correlation coefficient above 0.6 Van Delden and Hinssen (2012):PVref f /( / p)ref, 2›u › as well. The statistics for the shear stress behaves simi- where ( / p)ref (the reference isentropic density) is larly (not shown). This confirms our expectation that determined for one hemisphere as the horizontal aver- there exists a relation between the stretching rate of the age of (2›u/›p) from latitude 108 to 908. We investigate

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TABLE 2. The correlation coefﬁcient R of the mean stretching rate and the mean of the geopotential height F, wind speed jvj, kinetic energy (KE), and equator-to-pole temperature difference DT2m, for raw and detrended data, in JJA and DJF for TR, NM, and SM. Values statistically signiﬁcant at the 95% level are marked by an asterisk.

Raw Detrended SM TR NM SM TR NM F JJA 850 hPa 0.41* 0.12 0.07 0.03 20.09 20.09 500 hPa 0.47* 0.42* 0.31* 0.07 0.13 20.09 300 hPa 0.56* 0.51* 0.32* 0.05 0.16 20.10 DJF 850 hPa 20.16 0.21 0.20 20.08 20.10 20.17 500 hPa 0.08 0.44* 0.37* 0.06 0.07 0.04 300 hPa 0.33* 0.52* 0.39* 0.05 0.09 0.09 jvj JJA 1000–100 hPa 0.30 0.28 0.20 20.03 0.20 0.24 850 hPa 0.58* 0.68* 0.40* 0.06 0.21 0.08 500 hPa 0.16 0.07 0.14 0.00 0.07 0.23 300 hPa 0.00 20.11 20.17 20.10 0.12 0.16 DJF 1000–100 hPa 0.73* 0.32 0.49* 0.19 0.31 0.57* 850 hPa 0.66* 0.76* 0.35* 0.11 0.48* 0.15 500 hPa 0.62* 0.03 0.31 0.16 0.19 0.53* 300 hPa 0.52 * 0.05 0.27 0.11 0.21 0.43* KE JJA 1000–100 hPa 0.03 20.05 20.09 20.12 0.10 0.20 850 hPa 0.41* 0.55* 0.25 20.05 0.12 0.01 500 hPa 20.05 20.26 20.17 20.15 20.09 0.13 300 hPa 20.14 20.23 20.26 20.016 0.05 0.20 DJF 1000–100 hPa 0.57* 0.11 0.30 0.01 0.23 0.40* 850 hPa 0.61* 0.62* 0.17 0.02 0.42* 0.04 500 hPa 0.47* 20.08 0.12 20.08 0.18 0.40* 300 hPa 0.38* 20.04 0.20 0.01 0.21 0.38* DT2m JJA 2 m 20.03 — 20.20 20.18 — 0.14 DJF 2 m 0.35* — 20.52* 20.32 — 20.29

the potential vorticity anomaly on two of the often used temperatures, both standardized over time. The corre- atmospheric levels in synoptic analysis, on the 315- and lations for these variables are weaker than for the rela- 330-K levels. The right column of Fig. 5 illustrates the tive vorticity, but they generally change in the same correlation coefficients of the stretching rate with the (positive) direction with time. The corresponding cor- absolute value of the potential vorticity anomaly. We relation coefficients are displayed in Fig. 7. The corre- find that, in contrast to the relative vorticity, the correlation coefficients are the largest in the tropics. In JJA in lation coefficients for the potential vorticity anomaly TR and NM the temperatures of the lower and upper considerably differ on different levels and can be both troposphere (i.e., T2m, T850hPa, and T300hPa) are the most negative and positive at any given level. closely related to the stretching rate, while in DJF the The results related to the geopotential heights, wind strength of the relationship is similar for all of the alti- speed, and kinetic energy are displayed in Table 2. The tudes investigated here. For SM the correlation co- correlation coefficients are in general lower than those efficient for the 850-hPa level is small in both seasons.1 for the absolute value of the relative vorticity and some As the equator-to-pole temperature difference is the of them are nearly zero. The correlation coefficients for driving force of the atmospheric circulation, we also the wind speed and kinetic energy confirm the expec- investigate the relation between the stretching rate and tation that the stretching is related to the velocity dif- DT2m (Table 2). In JJA the correlation coefficients for ferences along the advected line segment rather than to SM and NM are found to be negative, falling below 20.2 the velocity values themselves. The correlation of the and are statistically not significant at the 95% level. In geopotential height with the stretching rate is the strongest at the 300-hPa level and significant at the 95% level in almost all of the three regions in both seasons. 1 This might be explained by the fact that because of Antarctica’s We repeated our calculations also for the 2-m tem- high orography the particles in this hemisphere cannot stay in the lower (higher pressure) layers of the atmosphere in this ex- perature T2m and the temperature T at selected pres- tended region. While reanalysis data are available for the lower sure levels. Figure 6 is the analog of Fig. 4: it shows the (higher pressure) levels like 1000 and 850 hPa, these levels are time series of the mean stretching rate and the mean often subterraneous.

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FIG. 7. The correlation coefﬁcient R of the mean stretching rate and the mean temperature with 95% conﬁdence intervals for different levels in (top) JJA and (bottom) DJF for TR, NM, and SM.

The change in the stretching rate of pollutant clouds is influenced by atmospheric structures like cyclones. More frequent or more intense cyclones imply a higher mean of the absolute value of the relative vorticity and the wind shear values and, therefore, an easier stretching of the pollutant filaments. Different reanalysis datasets provide slightly different, but correlated, results concerning the changes in cyclone properties (e.g., Tilinina et al. 2013; Kelemen et al. 2015). Although previous studies on the trends in the number and intensity of FIG. 6. The time evolution of the mean stretching rate h and the s extratropical cyclones reported trends of different signs mean temperature Ts, both standardized over time, for different pressure levels in JJA for (top) SM, (middle) TR, and (bottom) NM. depending on the geographical location (e.g., Gulev et al. 2001; Graham and Diaz 2001; Fyfe 2003; Wang et al. 2006; Ulbrich et al. 2009; Wang et al. 2013), the contrast to JJA, in DJF the corresponding correlation more recent studies concluded that the cyclonic activity coefficients are significant and have the opposite signs: increased since the 1980s in both hemispheres (Tilinina 0.35 and 20.51 for SM and NM, respectively. This might et al. 2013; Wang et al. 2013). Most of the papers suggest be the consequence of the observed difference in the decreasing trends in the midlatitudes of both hemi- trends: an increasing DT2m in the Southern Hemisphere, spheres and increasing trends in the high latitudes but a decreasing DT2m in the Northern Hemisphere. (Serreze et al. 1997; McCabe et al. 2001; Geng and Sugi

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2001; Lim and Simmonds 2007, 2009; Ulbrich et al. 2009; Wang et al. 2013). The overall increase of cyclonic activity is in agreement with our ﬁndings of positive trends in the stretching rates. Our results concerning the weaker link between the stretching rate of pollutant clouds and the mean temperature are in accordance with the ﬁndings of previous studies, in which cyclone frequency was found to be weakly correlated with the mean temperature (Agee 1991; Serreze et al. 1997; McCabe et al. 2001). The result that the mean stretching rate increases in both hemispheres—despite the opposite trend of

DT2m—may be explained by the fact that the effect of the change in the meridional temperature difference is complex and has diversified impacts (Hassanzadeh et al. 2014). The correlation analysis hitherto described revealed that for most of the investigated quantities the mean values change similarly. To check if the shifts of the mean values due to climate change influence the correlations, we repeat the correlation analysis for the time series of the quantities after removing a linear trend. As expected based on Fig. 4, we find a relatively strong connection between the fluctuations of the absolute value of the relative vorticity and the stretching rate. Figure 8 shows that in almost all cases, the correlation coefficient is above 0.4 and can reach as high a value as 0.7. The correlation coefficients between the detrended temperature and stretching rates are below 0.3 and can even become slightly negative (not shown). The corre- FIG. 8. The correlation coefficient R of the detrended mean lation coefficients for the remaining quantities are de- stretching rate and the detrended mean of the absolute value of the relative vorticity with 95% confidence intervals for different levels termined in the same way. The last three columns of in (top) JJA and (bottom) DJF for TR, NM, and SM. Table 2 show that none of these quantities are as strongly correlated with the stretching rate as the relative vorticity. To conclude, this new analysis provides We found a slight increase (3%–10%) in the values of further evidence that the intensity of the stretching of the mean stretching rates in the three studied geo- the pollutant clouds and the complexity of their evolv- graphical regions (tropics and SH and NH extratropics) ing structure are most closely related to the relative from 1979 to 2015. This increase of the mean stretching vorticity field. rate is equivalent to an increase of the characteristic length of the filaments by a factor of 1.2–1.65 over a period of 10 days. Larger stretching rate values indicate a 4. Summary more intense spreading, more foldings, and a larger For a simple characterization of the large-scale geographical area covered by the pollutants. The in- spreading of pollutant clouds, a quantity called topological creased mean stretching rate of the analyzed decades, entropy and well known in dynamical systems theory is therefore, implies the risk of a larger polluted region used. In this particular context, the topological entropy is from a particular pollution event. the rate of the exponential stretching of filament-like Finding a relationship between the stretching rate and pollutant clouds. As a measure of folding, it is also the meteorological variables could help estimate the closely related to the complexity and predictability of the changes of large-scale transport properties of the at- pollutant clouds. In the tropics, pollutant line segments mosphere for the different climate projections without stretch by a factor of 20–150 within 10 days, while in the the necessity to carry out computationally costly extra mid- and high latitudes the characteristic values of length transport simulations. For example, one would naively increase are between 300 and 3000. think that there is a definite connection between the

Unauthenticated | Downloaded 09/26/21 02:18 PM UTC DECEMBER 2017 H A S Z P R A 4239 meridional temperature difference and the intensity of Graham, N. E., and H. F. Diaz, 2001: Evidence for intensifica- spreading (characterized by the stretching rate), but the tion of North Pacific winter cyclones since 1948. Bull. analyzed data do not support this assumption. We found Amer. Meteor. Soc., 82, 1869–1893, https://doi.org/10.1175/ 1520-0477(2001)082,1869:EFIONP.2.3.CO;2. that the areal mean of the absolute value of the relative Gulev, S., O. Zolina, and S. Grigoriev, 2001: Extratropical cyclone vorticity for the atmospheric layer between 1000 and variability in the Northern Hemisphere winter from the 100 hPa, or for a single pressure level in the free atmo- NCEP/NCAR reanalysis data. Climate Dyn., 17, 795–809, sphere, is well correlated with the stretching rate. This https://doi.org/10.1007/s003820000145. correlation is much stronger than those for the temper- Hassanzadeh, P., Z. Kuang, and B. F. Farrell, 2014: Responses of midlatitude blocks and wave amplitude to changes in the ature, geopotential height, wind speed, kinetic energy, meridional temperature gradient in an idealized dry GCM. and potential vorticity. Geophys. Res. Lett., 41, 5223–5232, https://doi.org/10.1002/ 2014GL060764. é Acknowledgments. The author thanks the useful dis- Haszpra, T., and T. T l, 2011: Volcanic ash in the free atmosphere: ó é A dynamical systems approach. J. Phys.: Conf. Ser., 333, cussions with and suggestions of G. Dr tos, T. T l, 012008, https://doi.org/10.1088/1742-6596/333/1/012008. and A. Várai. P. Csomós,M.Herein,M.Vincze,and ——, and ——, 2013a: Escape rate: A Lagrangian measure of par- T. Weidinger are also acknowledged for valuable com- ticle deposition from the atmosphere. Nonlinear Processes ments and remarks. The author thanks one of the anony- Geophys., 20, 867–881, https://doi.org/10.5194/npg-20-867-2013. mous referees for the suggestions on wording. 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